This article analyzes data processing problems for training a neural network. The first stage of model training - feature extraction - is discussed in detail. The article discusses the method of mel-frequency cepstral coefficients. The spectrum of the voice signal was plotted. By multiplying the vectors of the signal spectrum and the window function, we found the signal energy that falls into each of the analysis windows. Next, we calculated the mel-frequency cepstral coefficients. The use of a chalk scale helps in audio analysis tasks and is used in training neural networks when working with speech. The use of mel-cepstral coefficients significantly improved the quality of recognition due to the fact that it made it possible to see the most informative coefficients. These coefficients have already been used as input to the neural network. The method with mel-frequency cepstral coefficients made it possible to reduce the input data for training, increase productivity, and improve recognition clarity.

Keywords: machine learning, data preprocessing, audio analysis, mel-cepstral coefficients, feature extraction, voice signal spectrum, Fourier transform, Hann window, discrete cosine transform, short Fourier transform

Using numerical modeling, we performed studies of the influence of the angle of inclination of the plates of the regenerative heat exchanger element on the heating time and pressure drop. The studies were conducted for models of heat exchange elements with lengths of 6 and 20 mm. Depending on the length of the element, the angle of inclination of the plates was: 10°, 20°, 30°, 40° (at L=6 mm) and 3°, 6°, 9°, 12° (at L=20 mm). At the boundary of the calculation area, the air flow velocity and temperature were established, namely 1 and 3 m/s, and 303 and 973 K. The research results demonstrated that increasing the angle of inclination of the plates helped reduce the heating time of the regenerator by 38.56-49.1%, depending on the length of the heat exchange element, the speed and temperature of the air flow.

Keywords: heat recovery, honeycomb heat exchanger, numerical modeling, calculation, heating time, pressure drop, heat exchanger geometry, angle of plate, air flow velocity, air flow temperature

This article examines the previously studied linear in factors and non-linear in parameters modular regression model containing unary module operations. Through the use of binary, ternary, ..., l-ary module operations, a generalization of modular regression was proposed for the first time. A special case of generalization is considered - regression with a multiary operation modulus. The problem of accurately estimating such a model using least absolute deviations is reduced to a mixed integer 0-1 linear programming problem. Using data on farm productivity built into the Gretl econometric package, classical linear regression and modular regression with a multivariate operation were built. The quality of approximation of the proposed modular regression turned out to be higher than the quality of the linear model.

Keywords: regression analysis, modular regression, least absolute deviations, multiary operation modulus, mixed integer 0-1 linear programming problem

Based on recent developments in the field of parallel computing, in particular at the SYCL abstraction level, the use of optimal parallel computing tools for building applications in the field of computational and applied mathematics is being considered. Examples are given of both simple computational algorithms and computations using mathematical libraries for computational linear algebra.

Keywords: parallel code,heterogeneous enviroment, intel data parallel c++, intel oneapi, sycl, onemkl, fpga accelerator, gpu accelerator

The article presents the development of a software tool for modeling the influence of physical processes occurring in a single-mode optical fiber as a result of bending deformation. Model of bending deformation of single-mode optical fiber is considered. Classical and refined models of deformation and their influence on the optical fiber params are given. The initial data required to implement the software tool is discussed in detail. The development of the modeling program was gradually considered. The specifics of the implemented program obtained during the computational experiment are indicated.

Keywords: mathematical modeling, optical fiber, bending deformation, modeling of deformed fiber behavior, computational experiment, software

The paper proposes mathematical models that make it possible to describe the electrical conductivity of a nanocomposite based on carbon nanotubes, taking into account the waviness effect and the dispersion index. The model takes into account the contribution of various parameters, such as the concentration of nanotubes, the length, diameter and orientation of the tubes, as well as the electrical properties of the nanocomposite matrix. Using the proposed model, numerical experiments were carried out to evaluate the effects of waviness and dispersion index on the electrical conductivity of the nanocomposite. Comparisons of model data with experimental data are presented, confirming the adequacy and accuracy of the model. The results obtained can be used to optimize the process of creating nanocomposites based on carbon nanoturbines, as well as to increase the efficiency of their use in various fields, including electronics and energy.

Keywords: mathematical modeling, software package, nanocomposites, electrical conductivity, carbon nanotubes, computational experiment

Skin cancer is the most common cancer pathology in the human body and one of the leading causes of death in the world. Artificial intelligence technologies can equal and even surpass the visual classification capabilities of a dermatologist. Thus, it is relevant to develop high-precision intelligent systems for auxiliary diagnostics in the field of dermatology to detect skin cancer in the early stages. The work proposes an ensemble intelligent system for analyzing heterogeneous dermatological data based on multimodal neural networks with various convolutional architectures. The accuracy of the weighted average ensemble model based on multimodal systems using convolutional architectures AlexNet, SeNet_154, Inception_v4, Densenet_161, ResNeXt_50 and ResNeXt_101 for 10 diagnostically significant categories was 87.38%.

Keywords: machine learning, artificial intelligence, convolutional neural networks, multimodal neural networks, ensemble neural networks, digital data processing, heterogeneous data, skin cancer, melanoma

Using numerical simulation, we carried out studies on the effect of the length of a porous heat exchanger on the deposition of dust particles. The heat exchanger models with lengths of 5, 10, 20 and 30 mm were the subject of the studies. At the boundaries of the computational domain, we set the air velocity at 0.1, 1, and 5 m/s and the diameter of dust particles from 10-7 to 10-4 m. Research results have shown that with increasing length of the porous heat exchanger, the efficiency of dust particle deposition increases. This can lead to a decrease in the thermal and hydraulic characteristics of the heat exchanger.

Keywords: porous media, heat exchanger, numerical simulation, calculation, deposition of dust particles, heat exchanger length, air flow velocity, particle diameter, air cooling, microelectronics

Methods of computer formation of the equations of motion of multibody systems with a tree structure and algorithms for their reduction to the normal form of ordinary differential equations are considered. The equations of motion are written using Hamilton's formalism for an extended set of state variables of a mechanical system. The equations are presented in a compact visual form. Recursive formulas for determining all coefficients of equations are written out. Algorithms for reducing these equations to Hamilton equations in generalized coordinates and generalized momenta are presented. An algorithm for solving the obtained equations of motion for multibody systems using the LTDL-elimination is presented. Formulas are written that allow one to calculate the amount of arithmetic operations required to bring the equations of motion to normal form using the considered algorithms. On the basis of these formulas, a comparative analysis of the efficiency of algorithms for rigid bodies systems of various structures and with various types of connections between bodies is carried out. The results of the analysis are presented in the form of diagrams. The diagrams highlight areas in which the advantage of one or another method is manifested, depending on the type of mechanical system.

Keywords: multibody systems, equations of motion, dynamics, canonical momenta, mathematical modeling, computational efficiency

The problem of flexible vibrations of a rectangular orthotorque plate clamped along the contour is considered. The general solution of the problem, which satisfies the vibartion equation identically, is constructed on the basis of the superposition method in the form of two Fourier series. Clamped boundary conditions lead to a homogeneous infinite system of linear algebraic equations with respect to unknown coefficients in the general solution. The uniqueness of a bounded non-trivial solution of an infinite system for the natural frequency is proved, the asymptotics of the unknowns are found, and an effective solution algorithm is constructed. Examples of the numerical implementation of the developed algorithm for calculating the natural frequencies and natural modes of the plate vibrations are given.

Keywords: plate, vibrations, natural frequencies, planar forces, superposition method, infinite system of linear equations, asymptotics

The construction and substantiation of a finite element model of the capillary tube running-in process, which was obtained by drawing on a fixed mandrel, are considered. The rolling rolls are cylindrical and absolutely rigid. The condition for performing the work is a comparison of the resulting gap between the pipe and the mandrel and the facet formed during deformation. The solid-state model of the process is described by an adaptive grid. Under these conditions, an informative model was obtained, which was used in parametric analysis.

Keywords: drawing with a mandrel, capillary tube, extraction, rolling, model construction, compression selection, pipe size tolerance

The paper deals with the construction of an algorithm for nonparametric estimation of the transition probability distribution density for the Markov model of the dynamics of the number of university employees. The problem of reconstruction of transition probability distribution density on a retrospective sample of small volume is solved. The result of the solution is the transition probability matrix, the elements of which are random variables with distribution laws obtained from retrospective data. A distinctive feature of the algorithm is the simultaneous consideration of regional and functional constraints on the values of transition probabilities. The convergence of the algorithm has been experimentally confirmed.

Keywords: probability density, nonparametric estimation, Markov model, simulation modeling, university staff movement, publication activity

The article presents studies of a computer simulation statistical model between the characteristics of flows in terms of linear density and the proportion of components in a mixed flow. The results of evaluating the effect of the filling fraction of the component on the average and standard deviation of the fraction of the 1st component in the mixture are presented, the type of autocorrelation functions of the linear density of the mixed stream and the fraction of the 1st component in the mixed stream are determined, estimates of the spectral density of dispersion for the linear density of the mixed stream and the fraction of the 1st component in the mixed stream are shown.

Keywords: fiber mixing, linear density, component fraction, autocorrelation function, spectral density of dispersion, standard deviation

This article considers the problem of determining the temperature field near a heat-loaded source in the form of a dipole field. Solving this problem will make it possible to identify general patterns of distribution of the temperature field as one moves away from the source. This will make it possible to ensure the normal functioning of powerful electronic components by ensuring the required intensity of heat flux removal, mainly in close proximity to a heat-loaded source, that is, in the zone of maximum heat flux density.

Keywords: numerical methods, energy saving, heat engineering, thermal conditions of equipment, heat-loaded source, near zone, numerical modeling, temperature field, thermal processes, finite element method

This study is devoted to the development of a new mathematical model, a wedge-shaped sliding support with a non-standard elastically deformed support profile of the slider surface, taking into account nonlinear factors, under conditions of a two-layer lubricant flow, providing effective lubrication and reducing wear of the working surface. To develop this model, we will use mathematical modeling and data analysis methods to take into account all the necessary factors and parameters. To achieve this goal, well-known nonlinear equations are used: the motion of a viscous incompressible fluid for a "thin layer", the continuity equation and the Lame equation with appropriate boundary conditions, taking into account the elasticity and adaptability of the support surface of the slider, as well as equality of velocities at the interface of stratified layers, equality of pressure at the ends of the interval and equality of velocities on the surface of the guide. As a result, the main performance characteristics of the ras were identified

Keywords: nonlinear factors, elastically deformed, non-standard surface, flow of two-layer lubricant, dependence of viscosity characteristics of lubricating layers, ratio of density characteristics

The article considers the problem of cryptanalysis of an information security system based on a difficult-to-solve problem of Diophantine equations. A mathematical model of such a protection system is described in the article and a solution to the cryptanalysis problem using an artificial immune system adapted for solving Diophantine equations is proposed. The paper discusses the basic principles of building artificial immune systems and presents the results of experiments on evaluating the effectiveness of the proposed system of Diophantine equations of a degree not exceeding six. The results obtained demonstrate the possibility of using artificial immune systems to solve the problem of cryptanalysis of information security systems based on Diophantine equations.

Keywords: cryptanalysis, information security system, diophantine equations, artificial immune system, adaptive algorithm, efficiency assessment

The effect of impurities on the conductivity of the allotropic modification of phosphorene (ε-P) was studied. The quantum chemical research package Quantum Espresso was used for calculations. The study was conducted on the basis of simulation modeling. Three-dimensional structures are modeled using Quantum Espresso. The work adapted the model for two-dimensional ε-phosphorene by choosing a unit cell vector so large that interaction between the layers was possible. It has been shown that S has the smallest changes. Significant changes in conductivity can be achieved by placing F in various configurations relative to the crystal lattice, which can be actively used to create differetnt types of detectors.

Keywords: phosphorene, allotrope, semiconductor, impurity, adsorption, conductivity, density functional theory, modeling, Quantum Espresso, crystal structure

The article describes a technique for constructing a non-fuzzy model for selecting contour points on an image. The technique includes the following steps: the formation of linguistic variables “pixel brightness difference” and “a sign that a pixel belongs to a contour”, the formation of a knowledge base of a neuro-fuzzy model using a binary image, the formation of a training set using both grayscale and contour images, training a neuro-fuzzy model using genetic algorithm. A feature of the presented genetic algorithm is - checking the conditions for the correctness of the values of the parameters of the membership functions obtained during the generation of chromosomes. Described the structure of a neuro-fuzzy model for making a decision about whether a pixel belongs to a contour. Presented the result of applying a neuro-fuzzy model for constructing image contours.

Keywords: neuro-fuzzy model, contour image, contour extraction, contour pixel, linguistic variable, fuzzy set, membership function, genetic algorithm, Tsukamoto inference, neuro-fuzzy model learning

This article presents a research study dedicated to the application of the YOLOv8 neural network model for road sign detection. During the study, a model based on YOLOv8 was developed and trained, which successfully detects road signs in real-time. The article also presents the results of experiments in which the YOLOv8 model is compared to other widely used methods for sign detection. The obtained results have practical significance in the field of road traffic safety, offering an innovative approach to automatic road sign detection, which contributes to improving speed control, attentiveness, and reducing accidents on the roads.

Keywords: machine learning, road signs, convolutional neural networks, image recognition

The problem of developing an intelligent automated system for detecting defects in textile materials is considered. An analysis of machine learning and deep learning algorithms was carried out in relation to solving the problem of product quality control. The implementation of an artificial neural network implemented in a Raspberry Pi microcomputer and receiving a set of input data in the form of a large stream of images from a high-speed digital camera is considered. The stages of creating a model in Python using the TensorFlow and Keras libraries are described. The development process includes the preparation of initial data intended for training and testing the system, as well as testing the operation of the resulting neural network, which consists in recognizing images of defects on fabric according to classification criteria.

Keywords: machine learning, neural network, defect images, textile material, training, testing, accuracy

The article describes a technique of developing neural network models of controllers for controlling a technical object, approximating the relationship between the control action and the deviation of the state of the object from the setting action, its speed and acceleration. The application of a technique for controlling the temperature of a water bath water heater is considered. The technical object is described by a second-order differential equation and has a smooth monotonic behavior.

Keywords: technical object, water bath, water heater, neural regulator, control, object behavior, model, neural network, training set, perceptron

The work is devoted to the study of the effect of electrical pulses on the processes of cisplatin transport through the plasma membrane. Technical devices based on the application of this technology are used to increase cellular uptake of cytotoxic agents within certain cancer treatment strategies. This article presents the results of mathematical modeling performed using computer methods that allow us to study the influence of different pulse parameters (amplitude, duration, frequency) on the efficiency of cisplatin transport. Numerical experiments using various difference schemes and mathematical models that take into account the physical properties of the plasma membrane have been performed. The results obtained allow us to better understand the mechanisms of the impact of electrical impulses on the processes of cisplatin transport, which may be of practical importance for the development of new methods of drug delivery and cancer treatment.

Keywords: mathematical modeling, software package, electroporation, cisplastin transport, plasma membrane, computational experiment

The task of planning the sending of messages of known volumes from source points to destinations with known needs. At the same time, it is assumed that the costs of transmitting information on the one hand are proportional to the transmitted volumes and the cost of transmitting a unit of information over the selected communication channels, and on the other hand are associated with a fixed subscription fee for the use of channels that does not depend on the volume of transmitted information. An indicator of the quality of the plan with such a statement is the total cost of sending the entire planned volume of messages. A comparative characteristic of the effectiveness of methods for obtaining optimal plans using a linearized objective function and an exact solution by one of the combinatorial methods is carried out.

Keywords: message transmission, transport task, criterion of minimum total costs, computational complexity of the algorithm, linearization of the objective function

The article describes a way to optimize the trajectory optimization process by replacing the edges of the trajectory with spatial Bezier curves with a Pythagorean hodograph.

Keywords: Algorithms for generating trajectories, methods for constructing the formation of UAV groups, mathematical models of UAVs, multi-agent systems, Bezier curves, Pythagorean hodograph

This article explores how to optimize Quantum Espresso for efficient use of Nvidia's graphics processing unit (GPU) using CUDA technology. Quantum Espresso is a powerful tool for quantum mechanical simulation and calculation of material properties. However, the original version of the package was not designed for GPU use, so optimization is required to achieve the best performance.

Keywords: Quantum Espresso, GPU, CUDA, compute acceleration